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Proposition: Prop. 11.18: Plane through Straight Line Perpendicular to other Plane is Perpendicular to that Plane

(Proposition 18 from Book 11 of Euclid's “Elements”)

If a straight line is at right angles to some plane then all of the planes (passing) through it will also be at right angles to the same plane.

• For let some straight line $AB$ be at right angles to a reference plane.
• I say that all of the planes (passing) through $AB$ are also at "right angles to the reference plane":bookofproofs$2212.

Modern Formulation

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Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1

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References

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016